Question : A solid cone of height 36 cm and radius of base 9 cm is melted to form a solid cylinder of radius 9 cm and height 9 cm. What percentage of the material is wasted in this process?
Option 1: 25
Option 2: 0
Option 3: 5
Option 4: 10
Correct Answer: 25
Solution :
Given: Height of the cone = 36 cm
Radius of base = 9 cm
Radius of cylinder = 9 cm
Height = 9 cm
The volume of cone = $\frac{1}{3} \pi r^2 h$
$=\frac{1}{3}\times \pi \times 9^2 \times 36=972\pi$ cm$^3$
Volume of cylinder = $\pi r^2 h$
$=\pi \times 9^2\times 9=729\pi$ cm$^3$
The volume of waste = volume of cone – volume of cylinder
$=972\pi - 729\pi=243\pi$
The material wasted = $\frac{\text{volume of cone – volume of cylinder}}{\text{volume of cone}}\times100$
= $\frac{243\pi }{972\pi}\times 100=25$%
Hence, the correct answer is 25.
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